diff --git a/pyerrors/fits.py b/pyerrors/fits.py
index 89f73e5b..675bdca6 100644
--- a/pyerrors/fits.py
+++ b/pyerrors/fits.py
@@ -365,6 +365,8 @@ def least_squares(x, y, func, priors=None, silent=False, **kwargs):
             if (chol_inv[1] != key_ls):
                 raise ValueError('The keys of inverse covariance matrix are not the same or do not appear in the same order as the x and y values.')
             chol_inv = chol_inv[0]
+            if np.any(np.diag(chol_inv) <= 0) or (not np.all(chol_inv == np.tril(chol_inv))):
+                raise ValueError('The inverse covariance matrix inv_chol_cov_matrix[0] has to be a lower triangular matrix constructed from a Cholesky decomposition.')
         else:
             corr = covariance(y_all, correlation=True, **kwargs)
             inverrdiag = np.diag(1 / np.asarray(dy_f))
diff --git a/tests/fits_test.py b/tests/fits_test.py
index 2eeb6a49..283ff6a2 100644
--- a/tests/fits_test.py
+++ b/tests/fits_test.py
@@ -223,6 +223,9 @@ def test_inv_cov_matrix_input_least_squares():
             diff_inv_cov_combined_fit.gamma_method()
             assert(diff_inv_cov_combined_fit.is_zero(atol=1e-12))
 
+        with pytest.raises(ValueError):
+            pe.least_squares(x_dict, data_dict, fitf_dict,  correlated_fit = True, inv_chol_cov_matrix = [corr,chol_inv_keys_combined_fit])
+
 def test_least_squares_invalid_inv_cov_matrix_input():
     xvals = []
     yvals = []